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Solutions to Homework #5
Chapter
22
54.
Picture the Problem:
Two currentcarrying wires each make a
contribution to the magnetic field at point P.
Strategy:
The magnetic field at point P is the vector sum of
the magnetic fields
1
2
and
B
B
r
r
from the two wires.
Use
equation 229 to find the magnitude and the RightHand Rule
to find the direction of each field.
Then add the two fields as
vectors in order to find the magnitude and direction of the net
magnetic field at P.
From the diagram we can see that
1
0.050 m,
r
=
(
29
(
29
(
29
2
2
2
1
0.050 m
0.050 m
2 0.050 m
2 ,
r
r
=
+
=
=
and that
2
B
r
points 45° below the −
x
axis.
Solution:
1.
Add the
two vectors using
equation 229 and the
RHR:
(
29
(
29
(
29
(
29
(
29
(
29
(
29
1
2
0 1
0 2
0
2
1
1
2
1
7
6
6
ˆ
ˆ
ˆ
ˆ
ˆ
ˆ
cos45
sin 45
2
2
2
2
2
2
4
10 T m A
4.0 A
ˆ
ˆ
ˆ
ˆ
ˆ
3.0 A
4.0 10
T
8.0 10
T
2
0.050 m
2
I
I
I
I
r
r
r
μ
π



=
+
=
+


=
+


=

+
=

B
B
B
x
y
x
x
y
x
B
x
x
y
x
y
r
r
r
r
2.
Find the magnitude of
:
B
r
(
29
(
29
2
2
6
6
6
4.0 10 T
8.0 10 T
8.9 10 T
8.9
T
B



=
+ 
=
=
3.
Find the direction of
:
B
r
6
1
1
6
8.0 10
T
tan
tan
63 below the dashed line to the right of
4.0 10
T
y
x
B
P
B
θ





=
=
=
Insight:
2
B
is smaller than
1
B
by a factor of
2
due to the farther distance of
2
I
from P, but is larger by a
factor of
4
3
due to the larger current.
The two effects nearly cancel out, making
2
B
only 5.7% smaller than
1
.
B
56.
Picture the Problem:
The number of turns in a solenoid is doubled, and at the same time its length is doubled.
Strategy:
Use
0
N
B
I
L
=
(equation 2212) to predict the change in the magnetic field that would result from
the indicated changes in the solenoid.
Solution: 1. (a)
Equation 2212 shows that doubling both the number of turns
N
and the length
L
of a solenoid
will have no effect upon the magnetic field produced by the solenoid.
We conclude that the magnetic field
within the solenoid would stay the same.
2. (b)
The best explanation is
III
. The magnetic field remains the same because the number of turns per length is
unchanged.
Statement I ignores the change in
L
, and statement II ignores the change in
N
.
Insight:
If the current in the solenoid were also doubled, the magnetic field strength would double.
82.
Picture the Problem:
A square loop of current and a straight
currentcarrying wire exert forces on each other.
Strategy:
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This note was uploaded on 02/10/2012 for the course PHY 102 taught by Professor Korotkova during the Spring '09 term at University of Miami.
 Spring '09
 KOROTKOVA
 Physics, Current, Work

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